Short two-qubit pulse sequences for exchange-only spin qubits in two-dimensional layouts
Jason D. Chadwick, Gian Giacomo Guerreschi, Florian Luthi, Mateusz Tomasz Mądzik, Fahd A. Mohiyaddin, Prithviraj Prabhu, Albert T. Schmitz, Andrew Litteken, Shavindra Premaratne, Nathaniel C. Bishop, A. Y. Matsuura, James S. Clarke
Exchange-only (EO) spin qubits in quantum dots offer an expansive design landscape for engineering scalable device layouts. The study of two-EO-qubit operations, which involve six electrons in six quantum dots, has so far been limited to a small number of possible configurations, and previous works lack analyses of design considerations and implications for quantum error correction. Using a simple and fast optimization method, we generate complete pulse sequences for , , i , leakage-controlled , and leakage-controlled two-qubit gates on 450 unique planar six-dot topologies and analyze differences in sequence length (up to 43% reduction) across topology classes. In addition, we show that relaxing constraints on postoperation spin locations can yield further reductions in sequence length; conversely, constraining these locations in a particular way generates a operation with minimal additional cost over a standard . We integrate this pulse library into the Intel quantum stack and experimentally verify pulse sequences on a Tunnel Falls chip for different operations in a linear-connectivity device to confirm that they work as expected. Finally, we explore architectural implications of these results for quantum error correction. Our work guides hardware and software design choices for future implementations of scalable quantum-dot architectures.
Exchange-only (EO) spin qubits in quantum dots offer an expansive design landscape for engineering scalable device layouts. The study of two-EO-qubit operations, which involve six electrons in six quantum dots, has so far been limited to a small number of possible configurations, and previous works lack analyses of design considerations and implications for quantum error correction. Using a simple and fast optimization method, we generate complete pulse sequences for , , i , leakage-controlled , and leakage-controlled two-qubit gates on 450 unique planar six-dot topologies and analyze differences in sequence length (up to 43% reduction) across topology classes. In addition, we show that relaxing constraints on postoperation spin locations can yield further reductions in sequence length; conversely, constraining these locations in a particular way generates a operation with minimal additional cost over a standard . We integrate this pulse library into the Intel quantum stack and experimentally verify pulse sequences on a Tunnel Falls chip for different operations in a linear-connectivity device to confirm that they work as expected. Finally, we explore architectural implications of these results for quantum error correction. Our work guides hardware and software design choices for future implementations of scalable quantum-dot architectures.
The implementation of high-fidelity quantum gates for spin qubits requires accurate control of exchange interactions between electrons confined in quantum dots, but pulse distortions can limit this control accuracy. Although linear-dynamical distortions can be compensated for by appropriately convolving the control signal, determining the necessary convolution requires detailed knowledge of the distortion's transfer function, and therefore the calibration of numerous parameters. Alternatively, control pulses can be designed to have a net-zero time integral canceling out linear-dynamical pulse distortions. We generalize net-zero pulse designs to quasi-zero pulses allowing net-positive but reduced time integrals. Using these pulse designs, we systematically develop complete gate sets for exchange-only qubits, and study the resulting tradeoffs between pulse duration, fidelity, and the required number of tunable parameters, both in simulation and experiment. We benchmark the optimized gate pulses on Intel's Tunnel Falls six-dot device and show they achieve fidelities similar to those obtained with a full filtering approach, with identical pulse durations and fewer tuning parameters. This reduction in complexity opens the door to fast and easily automated calibration schemes compatible with large-scale commercial quantum devices.
The benefit of exchange-only qubits compared to other spin-qubit types is the universal control using only voltage-controlled exchange interactions between neighboring spins. As a compromise, qubit operations have to be constructed from nonorthogonal rotation axes of the Bloch sphere and result in rather long pulsing sequences. This paper aims to develop a faster implementation of single-qubit gates using simultaneous exchange pulses and manifests their potential for the construction of two-qubit gates. We introduce pulse sequences in which single-qubit gates could be executed faster and show that subsequences on three spins in two-qubit gates could be implemented in fewer steps. Our findings can particularly speed up gate sequences for realistic idle times between sequential pulses and we show that this advantage increases with more interconnectivity of the quantum dots. We further demonstrate how a phase operation can introduce a relative phase between the computational and some of the leakage states, which can be advantageous for the construction of two-qubit gates. In addition to our theoretical analysis, we experimentally demonstrate and characterize a simultaneous exchange implementation of X rotations in a Si Ge quantum dot device and compare to the state of the art with sequential exchange pulses.
Exchange-only (EO) qubits, implemented in triple-quantum-dot systems, offer a compelling platform for scalable semiconductor-based quantum computing by enabling universal control through purely exchange interactions. While high-fidelity single- and two-qubit gates have been demonstrated, the synthesis of efficient multiqubit operations—such as the Toffoli gate—remains a key bottleneck. Conventional gate decompositions into elementary operations lead to prohibitively long and error-prone pulse sequences, limiting practical deployment. In this work, we introduce a gradient-based optimization algorithm, Jenga-Krotov (JK), tailored to discover compact, high-fidelity EO gate sequences. Applying JK to the Toffoli gate, we reduce the number of required exchange unitaries from 216 (in direct decomposition) to 92, and compress the time steps required from 162 to 50, all while maintaining target fidelity. Under realistic noise, the accumulated gate error from our optimized sequence is an order of magnitude lower than that of conventional approaches. We have also applied the JK algorithm to other multiqubit gates and algorithm. For the Fredkin gate, it reduces the number of time steps from 200 to 104 and the number of exchange unitaries from 276 to 172. For the quantum Fourier transform, it compresses the sequence from 180 to 80 time steps and from 237 to 202 exchange unitaries. These results demonstrate that the JK algorithm is a general and scalable strategy for multiqubit gate synthesis in EO architectures, potentially facilitating realization of multiqubit algorithms on semiconductor platforms.
Abstract In conventional exchange-only (EO) spin qubit demonstrations, quantum gates have been implemented using sequences of individually pulsed pairwise exchange interactions with only one exchange coupling active at a time. Alternatively, multiple non-commuting exchange interactions can be pulsed simultaneously, reducing circuit depths and providing protection against leakage. We demonstrate high-fidelity quantum control of an always-on exchange-only (AEON) qubit, operated using simultaneous exchange pulses in a triangular quantum dot (QD) array. We use blind randomized benchmarking to characterize the performance of the full AEON single-qubit Clifford gate set, achieving an average Clifford gate fidelity F C1 = 99.86%. Extensions of this work may enable more efficient EO two-qubit entangling gates as well as the implementation of native i -Toffoli gates in Loss-DiVincenzo single-spin qubits.
The growing interest in quantum computers has triggered various approaches for the realization of a large-scale quantum processor that can eventually outperform classical high-performance computers. Quantum computers are attracting increasing attention for their potential to enormously accelerate the simulation of quantum systems and the solution of optimization problems, promising an immense impact, particularly in fields such as chemistry, medicine, and cybersecurity. Although it is still a long way to a practical quantum device, the progress over the last decades has shown encouraging results for a so far limited number of quantum bits, or qubits for short, which represent the computational units of the processor. One promising platform for the implementation of qubits is the spin of charge carriers in semiconductor quantum dots. Especially the use of purified silicon as a host material has significantly improved the performance of quantum operations. Advanced fabrication techniques from the established semiconductor industry in principle allow for the manufacturing of a large number of qubits on a small chip, making them specifically competitive from the perspective of scalability. In this thesis, we investigate challenges for electron spin qubits, particularly in the context of scaling to large qubit arrays for quantum computation. We evaluate the performance of quantum gates, present error mitigation strategies, and propose new quantum operations for two particular spin qubit implementations. In a dense array of Loss-DiVincenzo spin qubits on a chip, quantum information can be electrically controlled by microwave pulses. For neighboring qubits, capacitive couplings of nearby electrodes lead to crosstalk that affects the quantum computation. The first examination in this thesis addresses the effect of crosstalk on idling and operating spin qubits due to an interfering microwave drive. After the analysis and characterization of the performance, we suggest mitigation protocols for different constellations of important quantum gates, which can be easily implemented experimentally. We further show how to reduce crosstalk in a two-qubit gate using an asymmetric driving scheme, resulting in an enormous improvement of the gate performance, and may be used to generally overcome the obstacle of crosstalk. An additional source of errors in spin qubit registers originates from the finite residual exchange interaction between neighboring qubits. It arises due to a finite overlap of the electron wave functions and is caused by the limited speed at which the applied voltages can be controlled. We evaluate the fidelity of doing quantum operations under these circumstances with a varying number of neighboring qubits and present robust mitigation schemes with a decent performance also in the presence of noise. Besides crosstalk, another crucial observation in experiments using microwaves is the heating caused by the delivery of high-power radio frequency pulses to the quantum chip and results in a change of the qubit properties. We therefore investigate the impact of phonons on the energy levels in spin qubits to identify a temperature-dependent correction to the qubit state splitting. As microwave pulses are associated with potential errors, exchange-only qubits represent a promising alternative to achieve universal quantum computation only using baseband control. Therefore, we shift our focus towards exchange-only qubits and outline the main error sources in these systems, including residual exchange interactions between spins, charge noise from the applied voltages, and magnetic fluctuations in the material. A consequential complication of this implementation is that the quantum information can leak out of the qubit states. This effect, however, can be reduced in the presence of a finite magnetic field, as we will demonstrate in this thesis. The gate construction for exchange-only qubits usually requires more pulse steps than in the previous qubit type. Nevertheless, if exchange interactions are switched on simultaneously, this can result in faster quantum gates, as we demonstrate in this thesis. Especially the discovery of a quantum operation that introduces relative phases between computational and leakage states can be of interest for the construction of two-qubit gates and will be discussed in an example for a special operation space.
Spin qubits in quantum dots provide a promising platform for realizing large-scale quantum processors since they have a small characteristic size of a few tens of nanometers. One difficulty of controlling, e.g., a few thousand qubits on a single chip is the large number of control lines. The crossbar control architecture has been proposed to reduce the number of control lines exploiting shared control among the qubits. Here we compile the surface code cycle to a pulse sequence that can be executed in the crossbar architecture. We decompose the quantum circuits of the stabilizer measurements in terms of native gates of the spin-qubit architecture. We provide a routing and scheduling protocol and construct a gate voltage pulse sequence for the stabilizer measurement cycle. During this protocol, coherent phase errors can occur on idle qubits, due to the operational constraints of the crossbar architecture. We characterize these crosstalk errors during the stabilizer measurement cycle and identify an experimentally relevant parameter regime where the crosstalk errors are below the surface code threshold. Our results provide design guidelines for near-term qubit experiments with crossbar architectures.